Short Answer:

The role of relative velocity in hydraulic machines is to show how fast the fluid moves with respect to the moving parts of the machine, like blades or vanes. It helps in understanding how fluid enters and exits the rotating parts, which is important for smooth operation and energy transfer.

Relative velocity is used to design blade angles, analyze flow direction, and reduce energy losses. It ensures that water enters the runner or impeller correctly, minimizing shocks and improving the overall efficiency and performance of turbines and pumps.

Detailed Explanation:

Role of Relative Velocity in Hydraulic Machines

In hydraulic machines such as turbines and pumps, relative velocity refers to the velocity of the fluid relative to the moving parts of the machine, such as the blades or vanes. It is a key factor in analyzing how the fluid interacts with the rotating components and helps engineers in designing machines for maximum efficiency.

Relative velocity is different from absolute velocity, which is the speed of fluid with respect to a stationary point. Since the blades in hydraulic machines are always rotating, it becomes necessary to understand how the fluid appears to move from the blade’s point of view, and this is what relative velocity explains.

1. Understanding Fluid Entry and Exit
   The smooth entry and exit of fluid into and from the rotating blades is essential in hydraulic machines.

• If the fluid enters the blade at the wrong angle due to incorrect relative velocity, it causes turbulence and shock.
• Correct matching of relative velocity with blade speed ensures smooth flow along the blade surface.
• This leads to better energy conversion and less wear on the machine.

The shape and angle of the blades are designed using the direction and magnitude of the relative velocity.

2. Use in Velocity Triangles
   Relative velocity is an important part of velocity triangles, which are used in fluid flow analysis.

• It helps determine how much energy is added or extracted from the fluid.
• It is used to calculate blade angles and to design the passage through which the fluid moves.
• The triangle includes three components: absolute velocity, blade velocity, and relative velocity.

The position and length of the relative velocity vector in the triangle show how effectively the blade and fluid interact.

3. Energy Transfer and Efficiency
   When fluid flows through a turbine or pump, it transfers energy to or from the rotating blades.

• Relative velocity affects how efficiently this energy transfer happens.
• If the fluid strikes the blade with the correct relative velocity, maximum energy is transferred with minimum loss.
• Improper relative velocity can lead to partial energy transfer and vibration.

In impulse turbines, like Pelton wheels, relative velocity is crucial in shaping the buckets so that water exits without causing reverse flow. In reaction turbines, it helps in guiding the fluid smoothly through the runner blades.

4. Helps in Avoiding Cavitation and Damage
   Cavitation is a condition where vapor bubbles form due to sudden pressure drops, often caused by improper fluid flow.

• By maintaining correct relative velocity, pressure changes can be controlled.
• This reduces the risk of cavitation and protects the machine components.

Also, uniform flow due to well-managed relative velocity decreases the chances of erosion and noise, increasing machine life.

Conclusion

Relative velocity plays an important role in hydraulic machines by describing the fluid motion relative to the moving blades. It is essential for designing blade angles, analyzing energy transfer, and achieving smooth, efficient, and safe operation of turbines and pumps. Without understanding relative velocity, machines may suffer from energy loss, cavitation, and mechanical wear.